# Math Help - Finding critical points in an equation with logarithmic expressions and exponents??

1. ## Finding critical points in an equation with logarithmic expressions and exponents??

So I'm trying to find the minimum and maximum values of this equation, and to do that I need to find the critical point(s).

f(x) = (x^5)(e^(6x))

I started by taking the derivative, using the product rule...

f'(x) = (5x^4)(e^(6x)) + (x^5)(6e^(6x))

If I set the left side to 0 I should be able to solve for x, but I have no idea where to begin!

2. Originally Posted by theant4
So I'm trying to find the minimum and maximum values of this equation, and to do that I need to find the critical point(s).

f(x) = (x^5)(e^(6x))

I started by taking the derivative, using the product rule...

f'(x) = (5x^4)(e^{6x}) + (x^5)(6e^{6x})

If I set the left side to 0 I should be able to solve for x, but I have no idea where to begin!
Factor!

$(5x^4)(e^{6x}) + (x^5)(6e^{6x})=x^4e^{6x}(5+6x)$